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Supporters who displayed Nazi symbols and salutes at the Australia Cup final "should be banned for life", a senior government official has said.

Football Australia (FA) said it "strongly condemns the actions of a small minority" of Sydney United 58 fans after opening disciplinary action.

New South Wales state Premier Dominic Perrottet said the behaviour of some supporters was "absolutely horrendous".

The club said it was "concerned" by reports of the actions of supporters.

In a statement, Sydney United 58 said it had "zero tolerance towards any form of disrespect, racism or discrimination".

The club added it would work with authorities to conduct a "full investigation".

Supporter attempts to drown out the Indigenous welcoming ceremony prior to kick-off at Western Sydney Stadium are also being investigated.

FA said on Monday it had issued a show-cause notice to semi-professional side Sydney United 58, this requiring the club to respond before any sanctions are implemented.

The governing body added it was working with New South Wales police "to determine strong and swift action on any identified anti-social behaviour".

Pictures on social media showed some Sydney United supporters making Nazi salutes during the match.

"It has no place, not just at sporting games, but anywhere in our state, and I know the police are looking at it," said Perrottet.

"Those people who have done that through those salutes should be banned for life."

The chanting and booing during the pre-match Welcome to Country - a practice of Aboriginal and Torres Strait Islander peoples - will be considered as part of the FA investigation.

"The incidents last night caused by some individuals and groups in the stadium was ignorant," said Jade North, chair of the Football Australia National Indigenous Advisory Group (NIAG).

"This type of behaviour was disrespectful and must not continue in our game and attitudes must change."

The first non A-League side to reach the final, Sydney United 58, formerly known as Sydney Croatia, lost 2-0 to Macarthur FC in front of a crowd of 16,461 on Saturday.

"The club is deeply committed to creating an environment that is respectful and inclusive, which allows our community members to celebrate their heritage in a meaningful and responsible way," the club's board said.

"Those that do not align themselves with these values are not welcome at Sydney United 58 FC and their views will never be tolerated."

FA said eight people were evicted during the match "to address some isolated behaviours by a small minority of individuals".